The monthly electric bill is given by C(x)=0.14x+75, where x represents the number of kilowatt hours of electricity used in a month. Give the slope of the bill function, the meaning of the slope, the y intercept, and the meaning of the y intercept.

To analyze the function $ C(x) = 0.14x + 75 $, where $ x $ represents the number of kilowatt-hours (kWh) of electricity used in a month and $ C(x) $ represents the monthly electric bill in dollars, we can break down the components of the function:

1. **Slope of the Bill Function:**
   The slope of the function is the coefficient of $ x $, which is $ 0.14 $. 

2. **Meaning of the Slope:**
   The slope represents the rate at which the electric bill increases per additional kilowatt-hour of electricity used. Specifically, for each extra kWh of electricity consumed, the bill increases by $0.14.

3. **Y-Intercept:**
   The y-intercept is the constant term in the function, which is $ 75 $.

4. **Meaning of the Y-Intercept:**
   The y-intercept represents the fixed part of the bill, which does not depend on the amount of electricity used. This could include base charges or fixed fees that are incurred regardless of electricity consumption. In this case, the minimum bill amount is $75, even if no electricity (0 kWh) is used.

Would you like a more detailed explanation of any of these points? Feel free to ask!

Here are five numbered questions you might consider:

1. How do you interpret the slope in a cost function context?
2. Can the slope of a function ever be negative in a billing scenario?
3. What other factors could contribute to the fixed charges represented by the y-intercept?
4. How would the function change if the cost per kWh increased?
5. How can you calculate the total cost for a specific amount of electricity used?

**Tip:** Understanding the slope and intercepts in linear functions is crucial for interpreting real-world scenarios, such as costs and charges, in a mathematical context.

Explore the function C(x) = 0.14x + 75, where x represents kilowatt-hours of electricity used monthly and C(x) represents the corresponding electric bill. Learn about the slope, y-intercept, and their meanings in the context of cost functions.

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